Middle term in expansion of {(1 + x)^{2n}} is

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7.Binomial Theorem

easy

The middle term in the expansion of ${(1 + x)^{2n}}$ is

A

$\frac{{(2n)!}}{{n!}}{x^2}$

B

$\frac{{(2n)!}}{{n!(n - 1)!}}{x^{n + 1}}$

C

$\frac{{(2n)!}}{{{{(n!)}^2}}}{x^n}$

D

$\frac{{(2n)!}}{{(n + 1)!(n - 1)!}}\,{x^n}$

Solution

(c) Middle term = ${T_{\frac{{2n + 2}}{2}}} = {T_{n + 1}} = {}^{2n}{C_n}{x^n}$= $\frac{{2n!}}{{{{(n!)}^2}}}\,.\,{x^n}$.

Standard 11

Mathematics

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